What is 7/13 plus 13/24? (Answer: 337/312)

Exact Answer

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Problem: What is 7/13 plus 13/24?
Formula / Expression: 7/13 + 13/24
Final Answer: 1 25/312 (337/312)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 24 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 24 = 312.
Working: LCD(13, 24) = 312

Step 2: Convert to Equivalent Fractions with Common Denominator 312
Multiply the numerator and denominator of 7/13 by 24, and multiply the numerator and denominator of 13/24 by 13 so both fractions share the common base 312.
Working: 7 × 24/13 × 24 = 168/312 and 13 × 13/24 × 13 = 169/312

Step 3: Add the Numerators
Now add the numerators (168 + 169 = 337) and keep the common denominator 312 unchanged.
Working: 168 + 169/312 = 337/312

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 337 and 312 is 1, confirming that 337/312 cannot be reduced further—it is already in its simplest irreducible form.
Working: 337/312

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (337) is greater than the denominator (312), divide 337 by 312: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/312.
Working: 337/312 = 1 25/312

Step 6: Decimal & Percentage Representation
Dividing the numerator 337 by denominator 312 produces a repeating decimal (approximately 1.080128, or 108.0128%).
Working: 337 ÷ 312 = 1.080128 (108.0128%)

Key Values:
- Simplified Fraction: 337/312
- Mixed Number Form: 1 25/312
- Decimal Value: 1.080128
- Percentage: 108.0128%

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Solved with FractionsCalc:
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7/13 + 13/24 = 337/312

Simplified Fraction

337/312

Mixed Number

1 25/312

Decimal Value

1.080128

Percentage

108.0128%

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Step-by-Step Solution: 7/13 + 13/24

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 24 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 24 = 312.

LCD(13, 24) = 312

Step 2

Convert to Equivalent Fractions with Common Denominator 312

Multiply the numerator and denominator of 7/13 by 24, and multiply the numerator and denominator of 13/24 by 13 so both fractions share the common base 312.

7 × 24/13 × 24 = 168/312 and 13 × 13/24 × 13 = 169/312

Step 3

Add the Numerators

Now add the numerators (168 + 169 = 337) and keep the common denominator 312 unchanged.

168 + 169/312 = 337/312

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 337 and 312 is 1, confirming that 337/312 cannot be reduced further—it is already in its simplest irreducible form.

337/312

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (337) is greater than the denominator (312), divide 337 by 312: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/312.

337/312 = 125/312

Step 6

Decimal & Percentage Representation

Dividing the numerator 337 by denominator 312 produces a repeating decimal (approximately 1.080128, or 108.0128%).

337 ÷ 312 = 1.080128 (108.0128%)

Visual Representation

The diagram below illustrates 7/13 plus 13/24 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`337/312`
Mixed Number Form	`1 25/312`
Decimal Form	`1.080128`
Percentage	`108.0128%`

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Frequently Asked Questions

What is 7/13 plus 13/24 as a fraction?

7/13 + 13/24 in simplest fraction form is 337/312 (or 1 25/312 as a mixed number).

What is 7/13 plus 13/24 as a decimal?

7/13 + 13/24 converted to a decimal is 1.080128.

What is 7/13 plus 13/24 as a percentage?

7/13 + 13/24 expressed as a percentage is 108.0128%.

How do you write 7/13 plus 13/24 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 337/312 can be written as the mixed number 1 25/312.

Does 7/13 plus 13/24 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.080128...) because the denominator contains prime factors other than 2 and 5.